Magnetic-field sensor with a back-bias magnet

ABSTRACT

An embodiment of a magnetic-field sensor includes a magnetic-field sensor arrangement and a magnetic body which has, for example, a non-convex cross-sectional area with regard to a cross-sectional plane running through the magnetic body, the magnetic body having an inhomogeneous magnetization.

This application is a continuation in part of U.S. patent applicationSer. No. 14/290,780, entitled “Magnetic-Field Sensor,” filed on May 29,2014, which is a division of U.S. patent application Ser. No.12/130,678, entitled “Magnetic-Field Sensor,” filed on May 30, 2008,which claims priority to German Patent Application No. 10 2007 025000.4, which was filed on May 30, 2007, all of which applications arehereby incorporated herein by reference.

TECHNICAL FIELD

Embodiments of the present invention relate to a magnetic-field sensorcomprising a magnet also referred to as a back-bias magnet.

BACKGROUND

In many fields of technology, magnetic-field sensors are employed todetect movements of objects, for example. In some applications, amagnetic field acting upon the magnetic-field sensor is influenced bythe movement of the respective objects such that conclusions may bedrawn in terms of the movement of the object on the basis of the changein the magnetic field detected by the magnetic-field sensor.

Examples are found, among others, in the field of automobileapplications, the movement of wheels being monitored in the context ofan ABS application (ABS=antilock system), for example, using respectivemagnetic-field sensors. Other applications in the field of automobiletechnology include observing or monitoring the movement of crankshafts,camshafts and other shafts in the field of motor vehicles.

Depending on the specific implementation of respective magnetic-fieldsensors, they comprise so-called back-bias magnets which are located ina fixed arrangement with regard to the actual magnetic sensor elementsof the magnetic-field sensor. In such a magnetic-field sensor, themagnetic field detected by the magnetic-field sensor itself may thus beat least partly caused by the back-bias magnet. The object whosemovement is to be monitored, for example, via the magnetic-field sensor,possibly influences and/or supplements, by magnets or magneticcomponents of its own, the bulk magnetic field which will then bedetected by the magnetic-field sensor.

Depending on the technology employed in the context of the actualmagnetic-field sensor elements, the back-bias magnets, which arefrequently implemented as permanent magnets, have differentrequirements. This may be accounted for, among other things, by the factthat some magnetic-field sensor element technologies are sensitive todifferent magnetic-field components, exhibit different responses tomagnetic fields, and comprise different magnetic-field boundariesspecific to the respective type.

SUMMARY OF THE INVENTION

One embodiment of a magnetic-field sensor comprises a magnetic-fieldsensor arrangement and a magnetic body which comprises a non-convexcross-sectional area with regard to a cross-sectional plane runningthrough the magnetic body, the magnetic body comprising inhomogeneousmagnetization.

A further embodiment of a magnetic-field sensor comprises amagnetic-field sensor arrangement, a first magnetic body comprising afirst magnetization direction, and a second magnetic body comprising asecond magnetization direction, the first and second magnetizationdirections differing from each other.

One embodiment of a method of producing a magnetic-field sensor includesproviding a magnetic body comprising a non-convex cross-sectional areawith regard to a cross-sectional plane running through the magneticbody, the magnetic body having an inhomogeneous magnetization, first andsecond spatial areas with regard to the magnetic body existing, so thatin the first spatial area, a magnetic flux density caused by themagnetic body is within a first flux density range, with regard to apredetermined spatial direction, and so that in the second spatial area,a magnetic flux density is caused by the magnetic body, with regard tothe predetermined spatial direction, which is within a second fluxdensity range, and arranging a magnetic-field sensor arrangementcomprising first and second magnetic-field sensor elements, so that thefirst magnetic-field sensor element is arranged in the first spatialarea, and the second magnetic-field sensor element is arranged in thesecond spatial area.

A further embodiment of a method of producing a magnetic-field sensorcomprises providing a first magnetic body having a first magnetizationdirection, and a second magnetic body having a second magnetizationdirection, the first and second magnetization directions differing, afirst spatial area and a second spatial area with regard to the firstmagnetic body and the second magnetic body existing, so that in thefirst spatial area, a magnetic flux density is caused by the firstmagnetic body and the second magnetic body with regard to apredetermined spatial direction, the magnetic flux density being withina first flux density range, and so that in the second spatial area, amagnetic flux density is caused by the first magnetic body and thesecond magnetic body with regard to the predetermined spatial direction,the magnetic flux density being within a second flux density range, andproviding a magnetic-field sensor arrangement comprising first andsecond magnetic-field sensor elements, so that the first magnetic-fieldsensor element is arranged in the first spatial area, and the secondmagnetic-field sensor element is arranged in the second spatial area.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will be detailed subsequentlyreferring to the appended drawings, in which:

FIG. 1a shows a cross-sectional view of a first embodiment of amagnetic-field sensor;

FIG. 1b shows a cross-sectional view of a further embodiment of amagnetic-field sensor;

FIG. 2 shows a schematic representation of a potential example of use ofan embodiment of a magnetic-field sensor;

FIG. 3a and FIG. 3b show cross-sectional views of further embodiments ofmagnetic-field sensors;

FIG. 4 shows a result of a numeric simulation of a resulting magneticfluid density in the case of an embodiment of a magnetic-field sensorand its back-bias magnet;

FIG. 5 shows a representation of an x component of the magnetic fluxdensity in the event of the back-bias magnet shown in FIG. 4;

FIGS. 6a and 6b show cross-sectional views of further embodiments ofmagnetic-field sensors;

FIG. 7 shows a result of a numeric simulation of a magnetic flux densityfor an embodiment of a magnetic-field sensor or of its back-bias magnet;

FIG. 8 shows a curve of x components of the magnetic flux density forthe numeric simulation shown in FIG. 7;

FIG. 9 shows a magnified representation of the curves shown in FIG. 8;

FIG. 10a and FIG. 10b show cross-sectional representations of furtherembodiments of magnetic-field sensors;

FIG. 11 shows a result of a numeric simulation with respect to amagnetic flux density of an embodiment of a magnetic-field sensor;

FIGS. 12a and 12b show various curves of x components of the magneticflux density for the numeric simulation shown in FIG. 11;

FIG. 13 shows a cross-sectional representation of a further embodimentof a magnetic-field sensor;

FIG. 14A illustrates a cross sectional view of a further inhomogeneousmagnet according to the present disclosure;

FIG. 14B illustrates a spatial view of an exemplary shape of the furtherinhomogeneous magnet;

FIG. 14C illustrates the inhomogeneous back-bias magnet in combinationwith a bare die sensor;

FIG. 14D illustrates a further implementation of the inhomogeneousback-bias magnet according to the present disclosure;

FIG. 15 illustrates a B_(x) component for an inhomogeneous and ahomogeneous magnetic field;

FIG. 16 illustrates a simulated distribution of magnetization for thefurther inhomogeneous magnet; and

FIG. 17 illustrates simulated B_(x) components for different angles αindicating different levels of inhomogeneous magnetization for thefurther magnet.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

FIGS. 1a to 13 show schematic representations of various embodiments ofmagnetic-field sensors with their magnetic bodies or back-bias magnets,as well as results of numeric simulations in the form of curves andother representations. However, before giving a more detaileddescription of a potential application scenario of a magnetic-fieldsensor in the context of FIG. 2, a description will initially be givenof a first embodiment of a magnetic-field sensor along with a magneticbody or back-bias magnet in the context of FIG. 1 a.

FIG. 1a shows a first embodiment of a magnetic-field sensor 100comprising a magnetic body or back-bias magnet 110 and a magnetic-fieldsensor arrangement 120. The magnetic body 110 in FIG. 1a comprises arecess 130 which faces the magnetic-field sensor arrangement 120 and hasa polygonal cross-section with regard to a cross-sectional plane runningthrough the magnetic body, as is depicted in FIG. 1 a.

Here, the recess 130 has a polygonal cross-section with a total of sevenvertices 140-1 to 140-7 in the embodiment shown in FIG. 1a . Unlike thecross-sectional shape of the magnetic body 110 which is shown in FIG. 1a, in other embodiments of a magnetic-field sensor 100, the recess 130 ofthe magnetic body 110 may also comprise a number of vertices 140 whichdeviates from seven. For example, in the case of a triangular recess,with respect to the respective cross-sectional plane running through themagnetic body 110, same could also comprise three vertices 140 only. Inprinciple, however, any number of vertices 140 may define the respectivecross-sectional shape of the recess 130 with respect to thecross-sectional plane.

In terms of the extension and the shape of the magnetic body 110perpendicular to the cross-sectional plane shown in FIG. 1a , arespective magnetic body 110 may comprise, for example, the samecross-sectional shape with regard to a cross-sectional plane whichprojects beyond the cross-sectional plane shown in FIG. 1a or isperpendicular to it. In other words, depending on the specificimplementation of the recess 130, the same shape of the recess withrespect to a cross-sectional plane running through a central point orany other designated point the may result. For example, in such a casethe set of all potential vertices 140 would form, with respect to aplane perpendicular to the plane shown in FIG. 1a , a circular and/or anellipsoidal set of points, or possibly a set of points which has theshape of a partial circle or partial ellipsis.

In other embodiments of a magnetic-field sensor 100, the magnetic bodies110 may exhibit other shapes of the recess 130 with respect to a planewhich is not the cross-sectional plane. For example, such a recess 130may comprise, with respect to a plane perpendicular to the plane shownin FIG. 1a , a cross-sectional shape deviating therefrom. Thus, it ispossible, for example, for the respective recess 130 being implementedin the shape of a groove within the magnetic body 110, so that in thiscase a respective cross-section through the respective magnetic body 110has, for example, a rectangular shape, a square shape or any other shapewhich is convex.

Of course, there are other configurations of a magnetic body 110 of anembodiment of a magnetic-field sensor 100, wherein the respectivecross-sections perpendicular to the plane shown in FIG. 1a also havepolygonal, ellipsoidal or any other cross-sectional shapes.

In addition, other configurations of a magnetic body 110 magnetized inan inhomogeneous manner may naturally also be employed in embodiments ofa magnetic-field sensor 100. For example, with regard to the straightconnecting line 160 drawn in as a dotted line in FIG. 1a , and/or withregard to the non-convex cross-sectional shape generally defined herein,the magnetic body 110 magnetized in an inhomogeneous manner may alsotake on a cross-sectional shape “to be regarded as a mirrored thereto”,as long as the magnetic body 110 is magnetized in an inhomogeneousmanner.

However, in the embodiments presented below, reference shall be madeparticularly to non-convex magnetic bodies 110 in order to simplify thedescription, the subsequent illustrations being applicable, however, toessentially all magnetic bodies 110 magnetized in an inhomogeneousmanner.

The magnetic body 110 as is depicted, for example, in FIG. 1a thuscomprises a non-convex cross-sectional plane 150 with respect to across-sectional plane running through the magnetic body 110. In thiscontext, a set of points within a plane, i.e., for example, also thecross-sectional areas such as the cross-sectional area 150, is convexprecisely when for any two points, respectively, of the respectivequantity it is true that also the direct straight connecting linebetween these two points runs entirely within the respective quantity,i.e., within the cross-sectional area 150. In other words, a quantitywithin a plane is convex precisely when all the potential straightconnecting lines of all the potential points of the respective quantityrun entirely within the quantity.

As was explained above, the cross-sectional area 150 of the magneticbody 110 is non-convex, since, for example, a straight connecting line160 drawn in as a dotted line in FIG. 1a , whose end points are bothlocated within the cross-sectional area 150, i.e., are elements of therespective quantity, however is not located entirely within therespective quantity, i.e., within the cross-sectional area 150. Rather,the straight connecting line 160 intersects the recess 130. Thecross-sectional area 150 is therefore non-convex, so that it may also bereferred to as concave. The terms concave and non-convex therefore maypossibly be used synonymously.

The magnetic body 110 of the embodiment of a magnetic-field sensor 100shown in FIG. 1a may be made from a permanent-magnetic material, forexample. Depending on the boundary conditions on which an embodiment ofa magnetic-field sensor is to be employed, i.e., not least with regardto potential temperatures of use, cost, useful magnetic fields and otherparameters, the magnetic body 110 may also be made, for example, fromiron, cobalt, nickel or other relatively complex compounds and alloys,which possibly include the above-mentioned metals as components. Inprinciple, respective magnetic bodies or back-bias magnets 110 may bemanufactured from ferrites, aluminum-nickel-cobalt (AlNiCo), alsosamarium-cobalt (SmCo) or neodymium-iron-boron (NdFeB). Of course, othermaterial combinations or materials are also feasible as a field ofapplication for the respective magnetic bodies 110.

As is indicated in FIG. 1a by the arrows 170, the magnetic body, or theback-bias magnet, 110 has an inhomogeneous magnetization. Themagnetization M of the magnetic body 110 here has been specificallygenerated to be inhomogeneous, various magnetizations occurring atvarious points, particularly within the cross-sectional area 150, whichdiffer at least with regard to their magnitudes or intensities and/ortheir directions.

In other words, a magnetization of a magnetic body is inhomogeneous whenit is largely not homogeneous, a homogeneous magnetization beingunderstood to mean, in the context of the present application, amagnetization which is constant and unidirectional with regard to itsdirection and intensity. Put differently, the magnetic body 110 has aninhomogeneous magnetization, as is shown by the arrows 170, since itsmagnetization does not have a constant direction and/or a constantmagnitude of the magnetization M, in the vectorial sense, across theentire magnetic body or across a substantial part of the entire magneticbody. In the context of the present application, a substantial portionof the entire magnetic body 110, or of the magnetic body 110, isunderstood to mean a volume fraction of the magnetic body 110 whichranges from 50% to 100%, i.e., for example, 95%, 90%, 80%, 75%, 70% or60%, it being possible for the respective volume fractions to result asa function of the respective field of application and implementations ofan embodiment of a magnetic-field sensor.

In addition, it should be noted here that for many magnets whichcomprise, in the entire volume, a magnetization which is constant interms of magnitude and direction, i.e., which are magnetized in ahomogeneous manner, the magnetic field resulting therefrom may beinhomogeneous both on the outside and inside of the magnet. In otherwords, the presence of an inhomogeneous magnetic field on the outsideand/or inside of a magnet need not be an indication that themagnetization, too, is inhomogeneous. In many cases, homogeneousmagnetizations are attractive particularly because they may bemanufactured in a comparatively simple and inexpensive manner.

The magnetic body 110, or the back-bias magnet 110, of the embodiment ofthe magnetic-field sensor 100 as is shown, for example, in FIG. 5a ,frequently comprises a remanent magnetic flux density ranging fromseveral hundred millitesla (≥100 mT) to several tesla (3 T), dependingon the example of use. Depending on the specific implementation andspecification of an embodiment of a magnetic-field sensor 110, themagnetic body 100 may thus comprise, for example, a “magnetization” or aremanent magnetic flux density Brem of typically 500 mT or 1 T, whichexists because of the magnetization. However, it should be noted in thiscontext that the above-mentioned flux density ranges are not to be takenin a limiting sense. Rather, they are merely examples as may be used insome fields of application of embodiments of a magnetic-field sensor100. In principle, other magnetizations may be used as a function ofvarious parameters, i.e., for example, of the technology of theindividual magnetic-field sensor elements, the dimensions of therespective magnetic-field sensor, and other parameters.

In addition to the magnetic body, or the back-bias magnet, 110, theembodiment of a magnetic-field sensor 100 shown in FIG. 1a alsocomprises the magnetic-field sensor arrangement 120 comprising, forexample, a substrate or a chip 180 and one or several magnetic-fieldsensor elements 190 as optional components. In the embodiment shown inFIG. 1a , the sensor arrangement 120 comprises at least twomagnetic-field sensor elements 190-1, 190-2 drawn in FIG. 1a . Dependingon the technology used, the magnetic-field sensor elements 190 may bemagneto-resistive sensor elements (xMR sensor elements), Hall sensorelements, or other sensor elements reacting to a magnetic influence,such as magnetic diodes or magnetic transistors.

With regard to the present invention, it should be noted that same maybe advantageously employed particularly with such sensors or sensorelements which exhibit saturation behavior, i.e., for example, with xMRsensor elements.

By contrast, Hall probes, for example, have virtually no saturation.However, since the amplifiers connected downstream from the Hall probeexhibit saturation behavior (because the amplifier becomes saturatedoutside its dynamic range), it may be advantageous also with Hall probesto use the magnetic bodies described here.

The magneto-resistive sensor elements include, among others, AMR sensorelements (AMR=anisotropic magneto resistance), GMR sensor elements(GMR=giant magneto resistance), CMR sensor elements (CMR=colossalmagneto resistance), EMR sensor elements (EMR=extraordinary magnetoresistance), TMR sensor elements (TMR=tunnel magneto resistance), orspin-valve sensor elements. Hall sensors may be horizontal or verticalHall sensors.

Depending on the specific implementation, the magnetic-field sensorarrangement 120 may comprise further components, such as an evaluatingcircuit, a sensor circuit or a respective encapsulating material forprotecting the individual magnetic-field sensor elements 190.

In some embodiments of a magnetic-field sensor 100, as is shown in FIG.1a , for example, the magnetization M has the following symmetryconditions with regard to a symmetry line 195, shown in FIG. 1a , at anx coordinate (x=0) with regard to the x component M_(x) of themagnetization M and to the y component M_(y) of the magnetization:M _(x)(x)=−M _(x)(−x)M _(y)(x)=M _(y)(x)  (1).

This means that the x component of the magnetization M_(x) has an oddsymmetry with regard to the symmetry line 195 at x=0, and that the ycomponent M_(y) has an even symmetry with regard to the x coordinate andthe symmetry line 195. More generally speaking, the magnetization M insome embodiments of a magnetic-field sensor has an odd symmetry relationwith regard to the associated magnetic body 110 with respect to acomponent, and has an even symmetry relation with regard to anothercomponent. More specifically, in some embodiments of a magnetic-fieldsensor, the magnetization M of the magnetic body 110 has an evensymmetry relation with regard to a vector component, and has an oddsymmetry relation with regard to a vector component perpendicular to thevector component.

Before further embodiments of magnetic-field sensors will be describedand explained in connection with FIGS. 1b to 13, it should be noted thatobjects, structures and components having identical or similarfunctional properties and features are designated by identical referencenumerals. Unless explicitly stated otherwise, the descriptions ofobjects, structures and components having similar or identicalfunctional properties and features may be interchanged. In addition, inthe further course of the present application, summarizing referencenumerals shall be used for objects, structures and components occurringseveral times in one embodiment in an identical or similar manner, oroccurring in different figures, embodiments in a similar manner, unlessfeatures or properties of a very specific object, structure or componentare explained and discussed. Utilization of summarizing referencenumerals therefore enables a more compact and clearer description of theembodiments of the present invention.

FIG. 1b shows a further embodiment of a magnetic-field sensor 100 whichdiffers only marginally from the embodiment shown in FIG. 1a . Theembodiment of a magnetic-field sensor 100 shown in FIG. 1b againcomprises a magnetic body 110, the magnetization M of which being againindicated by the arrows 170. In the embodiment depicted in FIG. 1b ,too, the magnetization M is inhomogeneous in a substantial portion ofthe magnetic body, as is shown by the course of the arrows 170. Morespecifically, the magnetization M of the magnetic body 110 again has thesymmetry conditions described in connection with equation (1).

Unlike the embodiments depicted in FIG. 1a , the magnetic body 110 ofthe embodiment of a magnetic-field sensor 100 shown in FIG. 1b has adifferent course with regard to an upper edge. More specifically, in theembodiment depicted in FIG. 1a , an upper edge of the magnetic body 110is delimited by a straight line, whereas in the magnetic body 110 inFIG. 1b , the magnetic body extends upward beyond the area representedin FIG. 1b . Irrespective thereof, however, in the magnetic bodydepicted in FIG. 1b , the cross-sectional area 150 is non-convex withregard to the cross-sectional plane reproduced in FIG. 1b , since thedirect straight connecting line 160, whose end points are located withinthe cross-sectional area 150, again itself intersects the recess 130,and thus is located within the cross-sectional area 150. In other words,irrespective of the upper shape or the outer shape, the cross-sectionalarea 150 of the magnetic body 110 is non-convex irrespective of thespecific shape of the outer, upper or lateral demarcation areas of themagnetic body 110.

In addition, the embodiment depicted in FIG. 1b differs with regard tothe recess 130. While in the embodiment shown in FIG. 1a it has apolygonal cross-section, in the embodiment shown in FIG. 1b , thecross-section of the recess shown there is ellipsoidal.

Apart from that, the embodiments of a magnetic-field sensor 100 shown inFIGS. 1a and 1b hardly differ. In the embodiment shown in FIG. 1b , across-section of the magnetic body 110 may comprise different shapes, asimilar shape or even the same shape with regard to a planeperpendicular to the cross-sectional plane shown in FIG. 1 b.

In both embodiments shown in FIGS. 1a and 1b , the magnetic-field sensorarrangement 120 is arranged, in relation to the magnetic body 110, suchthat the arrangement 120 is ideally also located such that is has acenter of gravity or central point of the magnetic-field sensorarrangement 120 on the symmetry line 195 as well. In addition, themagnetic-field sensor arrangement 120 ideally is aligned, in relation tothe symmetry line 195, such that a connecting line, not drawn in FIGS.1a and 1b , of the two magnetic-field sensor elements 190 shown thereintersects the symmetry line 195 at right angles. In other words, themagnetic-field sensor arrangement 120 ideally is arranged such that samereplicates or adopts the above-described symmetry of the magnetization Mof the magnetic body 110. Of course, in case of real implementations ofa respective embodiment of a magnetic-field sensor 100, deviations mayoccur with respect to the shifts in the x direction and/or in the ydirection and with respect to a rotation about any of these axes or anyaxis perpendicular to same.

As will be explained in the further course of the present application,it is this very above-described inhomogeneous magnetization M of themagnetic body 110, in connection with its cross-sectional shape in someembodiments of a magnetic-field sensor while taking into account thetechnology used of the magnetic-field sensor elements 190, that enablesan improvement of an increase in the positional tolerance of themagnetic-field sensor arrangement 120 with regard to the magnetic body110. In other words, in some embodiments of a magnetic-field sensor 100,a larger tolerance may be achieved with respect to the precise layout ofthe magnetic-field sensor arrangement 120 without having to accept, insubsequent operation of the embodiment of the magnetic-field sensor 100,disadvantageous effects concerning accuracy of measurement,functionality or other parameters which may possibly be caused bymagnetic-field sensor elements 190 which are disadvantageouslypositioned in relation to the magnetic body 110.

Especially in the case of magneto-resistive magnetic-field sensorelements 190, in some embodiments of a magnetic-field sensor 100 it maybe advantageous to implement a magnetic body 110 as is included in theframework of an embodiment. As will be explained below, in someembodiments overdriving of the respective magneto-resistive sensorelements 190 may possibly be inhibited, and/or the positioning toleranceof the respective sensor elements may possibly be increased, while no orhardly any negative consequences are to be expected for the actualmeasuring operation.

FIG. 2 shows a typical field of use of an embodiment of a magnetic-fieldsensor 100 in connection with determining a rotating rate, or rotatingspeed, of a shaft. More specifically, FIG. 2 shows an embodiment of amagnetic-field sensor 100 comprising, in addition to a magnetic body110, which may be implemented as a permanent magnet, for example, and tothe magnetic-field sensor arrangement 120, a protective casing includedin the magnetic-field sensor 100. As was already explained above, themagnetic-field sensor arrangement 120 additionally comprises twomagnetic-field sensor elements 190, which may be magneto-resistive,magnetic sensitive sensor elements, for example. As was explained above,the magnetic body 110 has been drawn in a simplified manner in FIG. 2without representing the above-explained features of the magnetic bodywith regard to the magnetization and the cross-section with respect tothe cross-sectional plane depicted in FIG. 2. The features were notreproduced in FIG. 2 merely so as to simplify the representation.

At a distance from a plane of the magnetic-field sensor elements 190,the distance being marked by an arrow 200 in FIG. 2 and also beingreferred to as a magnetic air gap, or air gap, a generator object 210 ismounted below the embodiment of the magnetic-field sensor 100, which isa toothed wheel, which sometimes also is referred to as a permeablegenerator wheel. Other generator objects 210 include drilled wheels,magnet wheels and other round or ellipsoidal objects suited, on accountof their choice of material and/or their topologies, to influence amagnetic field, which has been generated by the magnetic body 110, whena movement of the generator object 210 occurs, and possibly to generatea magnetic flux density themselves in the case of a magnet wheel.

Depending on the specific implementation and application scenario, anembodiment of a magnetic-field sensor 100 may also be employed inconnection with other generator objects 210. For example, a respectiveembodiment may be employed in connection with a magnet rod, drilled rod,or rack as the generator object 210, for example, to detect linearmovement or render it detectable. In very many cases, the generatorobjects 210 comprise a periodic structure with regard to themagnetization, the topology or other features, so that in the case of amovement of the generator objects 210, a periodic change in the magneticfield (among others, that of the magnetic body 110) is caused. Therespective generator objects 210 are frequently implemented either aspart of a respective moving component, or are connected to same.

In the case of a toothed wheel as the generator object 210, as is shownin FIG. 2, same may be coupled, for example, to a shaft, i.e., acrankshaft or a camshaft, or to a wheel. If the generator object 210 ismoved, i.e., in the case of the toothed wheel depicted in FIG. 2, isrotated, as is indicted by the arrow 220, this causes a change in themagnetic field which may be detected by the magnetic-field sensor 100.

Depending on the goal envisaged in the field of applying an embodimentof a magnetic-field sensor 100, movements of wheels may thus bedetected, for example, by means of magnetic sensors, as may be desired,for example, in the context of an ABS system. Other embodiments of amagnetic-field sensor 100 may be employed, for example, in the field ofengine control and monitoring, e.g., as crankshaft sensors or camshaftsensors. In this context, toothed wheels 210, among others, are used inconnection with small permanent magnets as magnetic bodies 110 on therear side of the actual sensors or of the magnetic-field sensorarrangement 120. Moving or rotating the wheel then results in asinusoidal magnetic field in the area of the magnetic-field elements190, the component of the magnetic field being evaluated at the chiplevel, or substrate level, in the case of magneto-resistive sensors (xMRsensors). At the same time, the direction of the rotary motion of thewheel may possibly also be evaluated and detected by a further sensor orby means of other technical measures.

In many applications, a small permanent magnet is thus mounted as amagnetic body 110 on a magnetic-field sensor arrangement 120, so thatboth may be arranged before a tooth-wheel shaped permeable disk, as isschematically depicted in FIG. 2. When the disk is rotated, the teeth ofthe toothed wheel 210 pass the plane of the magnetic-field sensorelements 190 at the distance of the magnetic air gap and thus generate asmall field variation which may be detected by the embodiment of themagnetic-field sensor 100 and which comprises information on the angularposition and the rotating speed of the disk. In many cases, the waveformof the magnetic-field variation is nearly sinusoidal, and its amplitudedrastically decreases as a function of an increasing (magnetic) air gap.

In the case of a toothed wheel as the generator object 210, as isdepicted in FIG. 2, the amplitude of the waveform frequently decreasesroughly exponentially, in proportion to a ratio of the magnetic air gapand the so-called pitch (possibly multiplied by a factor of 2π). In thiscontext, the so-called pitch is defined as the quotient of half thecircumference of the toothed wheel, divided by the number of teeth ifsame are equidistantly distributed across the circumference of thetoothed wheel. Thus, the pitch represents half the period of the toothedwheel. For this reason, it may be advisable, in some embodiments of amagnetic-field sensor 100 and in various fields of application of same,to operate embodiments as close to the generator object 190 as possibleso as to bypass and to prevent, e.g., magnetic air gaps larger thanapproximately the width of a tooth. An increase in the magnetic air gapfrom about the width of one tooth to about 150% of the width of a toothmay reduce a magnetic field amplitude by more than a factor of 5, forexample, depending on the specific circumstances. For example, theamplitude depends on exp(−2Pi*z/lamda), lamda being the magnetic period,i.e., lamda/2 is a width of a tooth, or a width of a gap between twoteeth. If z=lamda/2 increases to z=1.5*lamda/2, the amplitudeconsequently will change by a factor of exp(−Pi)/exp(−Pi*1.5)=4.8.

In the case of magneto-resistive sensor elements, i.e., for example, GMRsensor elements 190, it may happen that a respective magnet arrangementoverdrives the individual GMR sensor elements 190 with regard to themagnetic-field components in the plane of the substrate or of the chip.In such a case, it may happen that the magnetic-field sensor element(s)190 concerned will not provide any measurement signals, or measurementsignals which are hardly usable.

Thus, even if, for example, the toothed wheel 210 is positionedsymmetrically to the chip of the magnetic-field sensor arrangement 120,i.e., if, for example, a tooth center or a gap center of the toothedwheel 210 is directly in a (xx=0) position also drawn in FIG. 2, it mayhappen that the flux lines of the magnet diverge, as a result of whichinadmissibly large Bx components will act upon the two(magneto-resistive) magnetic-field sensor elements 190 shown in FIG. 2.As was already explained in connection with FIGS. 1a and 1b , the (x=0)position here is defined by the symmetry line 195, which in connectionwith FIG. 2 relates to the position located precisely between the twomagneto-resistive sensor elements 190 shown in FIG. 2.

In such a case, both magneto-resistive sensor elements 190 are driveninto saturation, and can no longer give off any (usable) signal. In someapplications wherein an embodiment of a magnetic-field sensor 100 isemployed, a common remanence of the magnetic bodies or back-bias magnets110 used is in a range of just above 1 tesla (T). Typical toothed wheelsas generator objects 210 comprise teeth and gaps approximately 3 mmwide, the depth of the gap also corresponding to about 3 mm. Of course,other dimensionings of respective toothed wheels or other generatorobjects may occur in other examples of use. Also, the respectiveembodiments of magnetic-field sensors 100 are not limited to thesevalues. It shall be noted in the context of the present invention thatlarge magnetic fields at the xMR element may be achieved, for example,using large magnets or using large remanences, or using a smalldemagnetization factor.

Depending on the specific application, the magneto-resistive sensorelements 190 are typically arranged within a range of about 1 mm beforethe magnet or magnetic body 110, and the toothed wheel itself isarranged about 1 to 4 mm before the magneto-resistive sensor elements190, so that the magnetic air gap is also within this range. In someapplications and, thus, in some embodiments of a magnetic-field sensor100, the magnetic or magnetic body 110 has a cross-section of 5 mm inthe x direction, and of 6 mm in the y direction, the magneto-resistivesensor elements 190 at the chip being spaced apart by about 2.5 mm. Insuch a case, it may happen that the Bx component of the magnetic fieldstrength on the right-hand one of the two magnetic-field elements 190ranges from about 95 to 117 mT, the different values resulting as afunction of the (magnetic) air gap. Accordingly, in the case of asymmetric layout, Bx components ranging from −95 to −117 mT act upon theleft-hand sensor element 190. Depending on the specific implementationof the magnetic-field sensor element 190, in particular in the case of aGMR magnetic-field sensor element, such a sensor element frequently hasa linear drive range of up to +/−15 mT. If such a GMR sensor element 190is highly overdriven by the magnet, it will no longer function in auseful manner and will no longer be able to provide useful measurementsignals.

With other GMR sensor elements 190 it may happen that they becomesaturated already at a magnetic flux density of about 10 mT. Thus, ifthere are magnetic-field components, or magnetic flux densitycomponents, of more than 100 mT at the location of the GMR sensorelements 190, the latter will be driven into saturation, so that smallsuperimposed alternating magnetic fields as may be caused by thegenerator object 210 are no longer detectable. It may therefore beuseful in such a case to reduce the above-described magnetic fluxdensity by a factor of 15.

If, for example, merely a modulation of between 12 mT and 14 mT iscaused by a tooth at a saturation field strength of about 10 mT of a GMRsensor element, the respective GMR sensor element in many cases may nolonger provide a usable output signal, so that the sensor overall may nolonger be able to detect the rotation of the generator object 210.

As was already explained above, the above numerical indications inparticular serve illustration and are not to be understood in a limitingsense. Embodiments of magnetic-field sensors 100 may be employed withina very wide range of magnets or magnetic bodies 110, and within a verywide range of different magnetic-field sensor elements 190. Also, in thecase of respective application scenarios, embodiments may be combinedwith very many different generator objects 210 so as to form speedsensors, for example, or other magnetic-based sensors.

FIGS. 3a and 3b show two further embodiments of magnetic-field sensors100. More specifically, the two embodiments are depicted along with agenerator object 210, respectively, it being possible for the generatorobject 210 to be a rack or a toothed wheel, for example, which isdepicted without any curvature in FIGS. 3a and 3b in order to simplifythe representation.

The embodiments of magnetic-field sensors 100 depicted in FIGS. 3a and3b thus each comprise a magnetic body 110 which again comprises, withrespect to the cross-sectional plane shown in FIGS. 3a and 3b , anon-convex cross-section having a recess 130, the recess 130 beingconfigured to be circular in the case of the embodiments shown in FIGS.3a and 3b . Of course, it may be noted in this context that thedesignations circular or ellipsoidal may also be applied to respectivesectors and portions of the respective geometric figures, i.e., of acircle or an ellipsis.

In the embodiments of a magnetic-field sensor 100 depicted in FIGS. 3aand 3b , the magnetic bodies 110, or the two back-bias magnets 110,again have an inhomogeneous magnetization, as is depicted by the arrows170 in both figures. Depending on the specific implementation of anembodiment, here, too, the magnetic-field sensor arrangement 120 maypossibly include a casing, also referred to as a package, in addition tothe chip or the substrate 180 and the (magneto-resistive) magnetic-fieldsensor elements 190, i.e., GMR magnetic-field sensor elements, forexample.

In the embodiments depicted in FIGS. 3a and 3b , the magnet or magneticbody 110 is configured as part of a ring, and is essentially radiallymagnetized, as is indicated by the arrows 170. More specifically, themagnetic body 110 here has an annular shape, but in other embodiments ofa magnetic-field sensor 100, it may also have other shapes, such as thatof a flat or upright ellipsis. As was already explained in the contextof FIG. 1b , it may suffice for the magnetic body 110 to comprise aninner recess so that the above-described magnetization of the magneticbody 110 may be performed. Basically, any outer demarcation curvedesired may thus be provided, in principle. As was explained before, insome embodiments of a magnetic-field sensor 100, the inner recess may becircular, ellipsoidal or polygon-shaped. In other words, in differentembodiments of a magnetic-field sensor, the magnetic body may have anon-convex cross-section or a non-convex cross-sectional area inrelation to a cross-sectional plane.

FIG. 3a thus shows an embodiment wherein the magnetic body 110 extendsover 180° and is configured as an annulus. By contrast, in theembodiment depicted in FIG. 3b , the magnetic body 110 depicted as anannulus extends over less than 180°. Depending on the specificimplementation, the magnetic body 110 may also extend over more than180°.

The sensor IC (IC=integrated circuit), or the magnetic-field sensorarrangement 120 may be moved, or shifted, both “to within the magnet”and to the area of the recess 130, as is depicted in FIG. 3a . In thecase of relatively small magnets 110, or even in the case of limiteddesign space, the magnet 110 may also be placed on the back of thesensor IC, wherein a front side and a bottom side of the IC 120 may beused equally well in many cases with regard to the fixing described,depending on the specific implementation of an embodiment of amagnetic-field sensor 100.

However, in many cases of application it may be advisable to move theGMR sensor elements 190 as close to the toothed wheel or the generatorobject 210 as possible, so that it may possibly be advisable in such acase to secure the magnet 110 on that side of the chip 120 whichcontains no components (e.g. the magnetic-field sensor elements 190). Insuch a case, it may thus be advisable to secure the magnetic-fieldsensor arrangement 120 to the magnetic body 110 such that it is rotatedby 180° in relation thereto as compared to the representation of FIGS.3a and 3b , i.e., to secure it in a precisely inverse manner to thatdepicted in FIGS. 3a and 3b . The magnetic-field sensor elements 190thus may be located such that they are rotated by 180° in relation tothe substrate 180 and the generator object 210.

Depending on the specific implementation, a typical dimension may thuscomprise, in the case of embodiments as are shown in FIGS. 3a and 3b ,an outside diameter of about 9 mm and an inside diameter of about 5 mmin relation to the shape of the magnetic body 110. A strength of theremanent magnetization again may be higher than about 500 mT or higherthan about 1 mT, depending on the specific implementation of anembodiment.

In some embodiments, the spacing between the two sensor elements 190 isabout the size of a tooth or a tooth gap of a generator object 210. Insome embodiments, or in some cases of application, this may be, forexample, 2.5 mm for the distance between the two outer sensor elementsshown in FIGS. 3a and 3b . Depending on the specific implementation, acentral sensor element may be employed, for example, for detecting thedirection, it being possible for the central sensor element to bearranged in the center between the left-hand and right-hand sensorelements. However, in some fields of application, other distancesbetween the sensor elements 190 are useful. Other distances, for example1.7 mm, may also be used.

The surface of the chip 180 in many cases is arranged at a distancebefore the magnet 110 ranging from about 0.5 mm to about 2 mm, distancesof about 0.7 mm frequently representing a useful compromise, since onthe one hand, the magnet 110 should be located as close as possible tothe chip 180, and thus, to the magnet wheel 210 and, on the other hand,a thickness of mounting components (package bottom, lead-framethickness, die-attach thickness, and silicon thickness) frequently is ina range of about 0.7 mm. A distance of the chip 180 from the generatorobject 210, also referred to as an air gap, may amount to several tenthsof a millimeter as a minimum, but as a maximum should not exceed aspacing of the width of about four teeth or four tooth gaps in somefields of application, since with larger air gaps, the magnetic fieldsignal amplitude will decrease exponentially.

FIG. 4 shows a result of a numerical simulation of a magnetic fieldstrength curve and of magnetic field lines as result in the case of amagnetic body 110 as is described in the context of FIG. 3a and theembodiment discussed there. Calculating magnetic fields, as have caused,for example, the magnetic field curve shown in FIG. 4, in many cases isanything but trivial and basically comes down to solving the fourMaxwell differential equations for electromagnetic fields. There areindeed simplified forms for special cases, which possibly may be solvedin a closed form, but specifically for calculating magnetic fields,magnetic flux densities and other curves and characteristics discussedin the context of the present application, numeric simulation, which maybe performed, for example, on the basis of a two-dimensional orthree-dimensional simulation using the finite elements method isgenerally indispensable. Respective simulations and calculations may beperformed, for example, on the basis of the equation

$\begin{matrix}{{B = {\mu_{0}{\int_{v}{\frac{{redMxdegrees}_{A}r}{4\pi\; r^{2}}{dV}}}}},} & (2)\end{matrix}$while taking into account the respective boundary conditions, B beingthe magnetic induction or the magnetic flux density as a vectorialquantity, μ0 designating the permeability of the vacuum, red Mdesignating the rotation of the (vectorial) magnetization, degreeA rdesignating the gradient of the positional coordinate with regard to thestarting point A, and r being the distance between the starting pointand the source point. Integration is performed across the entire space,i.e. not only within the material of the magnetic body 110, but alsoacross its surface, which is indicated by the “integration boundary” Vin equation (2).

In addition to the magnetic body 110, FIG. 4 also schematically depictsthe generator object 210 shown in FIGS. 3a and 3b . In addition to amultitude of field lines 230, for some areas, the respective magneticflux density of between 0.2 T to a maximum of 0.5 T is additionallydepicted in FIG. 4. Here, an arrow 240 in the inner part of therepresentation in FIG. 4 marks a decrease of the magnetic field strengthas is depicted by an arrow 250 in the area of the legend.

FIG. 4 thus represents the cross-section of the magnetic body in theform of an annulus extending over 180° and being magnetized in theradial direction, as was already described in connection with FIG. 3a .The toothed wheel as the generator object 210 here is positionedsymmetrically to the magnet 110. In this position, the Bx component ofthe magnetic flux density at the location of the magnetic-field sensorelements 190 (not shown in FIG. 4) should ideally be as close to zero aspossible, but at least within the linear control range of a GMR sensorelement, i.e., for example, between approx. −15 mT and +15 mT.

The result, shown in FIG. 4, of a numeric simulation is based on, withregard to the magnetic body 110, a remanence of 1 T of the magnetic body110, the remanence extending homogeneously across the entire magneticbody 110 in terms of magnitude. However, the direction of themagnetization, which due to its radial nature is inhomogeneous, isexempt therefrom.

In addition, FIG. 4 has horizontal lines 260 drawn in between the endfaces of the magnet, in the area of the lines 260, the magnetic fieldstrength Bx having been evaluated as a function of the x coordinate inthe context of the curves represented in FIG. 5 which follows.

FIG. 5 depicts a total of eleven curves 270-1 to 270-11 reproducing themagnetic flux density Bx in tesla (T) for the lines 260 represented inFIG. 4. The curves 270 here correspond, in an ascending order, to theirnumbers which are indicated after the hyphen in the context of thereference numerals, to the y positions y=−0.5 mm, −0.4 mm, −0.3 mm, −0.2mm, −0.1 mm, 0 mm, +0.1 mm, +0.2 mm, +0.3 mm, +0.4 mm, +0.5 mm.

The curves 270 show that due to the symmetry of the arrangement, the xcomponent of the magnetic flux density Bx versus the x coordinate xalmost vanishes for the case of y=0 (curve 270-6), and thus wouldrepresent a basically ideal position for the GMR sensor elements. If,for example, the magnetic-field sensor elements 190 are positioned suchthat they are symmetrically distributed around x=0 at a distance of 1.25mm, i.e., at the x positions x=+/−1.25 mm, y positions ranging fromy=−0.1 mm to y=+0.1 mm are quite suited to ensure x components of themagnetic field strength of, in terms of magnitude, less than 20 mT(|Bx|<20 mT), as the curves 270-5, 270-6, 270-7 for the y positionsy=0.1 mm, 0 mm, +0.1 mm show. The curves 270 essentially comprise amirror symmetry with regard to the point (x, Bx)=(0 m, 0 T). As comparedto a simple cubic magnet having a continually homogeneous magnetization,a reduction of the x component of the magnetic flux density Bx may thusbe achieved by employing an embodiment of a magnetic-field sensor 100,it sometimes being possible for the reduction to amount to as much asone order of magnitude.

FIGS. 6a and 6b show further embodiments of a magnetic-field sensor 100which are similar to the embodiments of FIGS. 3a and 3b , but differfrom same in that the magnetic bodies 110 are magnetized in an azimuthalmanner, as is indicated by the arrows 170. With this possibility of anembodiment of a magnetic-field sensor 100, the magnetic body 110 may, asis depicted, for example, in FIG. 6a , comprise an annular cross-sectionextending over 180° C. Likewise, as is depicted in FIG. 6b , it maycomprise a cross-section extending over less than 180°. The magnet 110of the embodiment shown in FIG. 6b may therefore be regarded as “cut offin the radial direction”, other shapes of the magnetic body 110 beingalso possible, of course. For example, magnetic bodies 110 wherein theend faces are cut off, for example, in the x direction or in the ydirection are also conceivable. As was already explained above in thecontext of FIGS. 1a, 1b, 3a, and 3b , the outer shape of the magneticbody is less decisive in this context. Therefore, other directions whichare oblique to the above-mentioned directions are also possible as“sectional directions” of the magnetic body 110.

Apart from the magnetization M as is depicted by the arrows 170 in FIGS.6a and 6b , the embodiments of a magnetic-field sensor 100 which areshown in the figures hardly differ, or do not differ at all, from theembodiments shown in FIGS. 3a and 3b in terms of the further components.For this reason, reference shall be made, particularly with respect tothe further components, to the respective descriptions thereof.

The magnetization of the magnetic body 110 as is depicted in FIGS. 6aand 6b thus obeys the following symmetry conditions with respect to thex component M_(x)(x) and the y component M_(y)(x):M _(x)(x)=M _(x)(−x)M _(y)(x)=−M _(y)(−x)  (3).

This means that in this case the x component of the magnetization has aneven symmetry relation with respect to the symmetry line 195 (x=0),whereas the y component of the magnetization in this case meets an oddsymmetry relation with respect to x. In this case, too, it may be statedin some embodiments of a magnetic-field sensor 100 that one of the twomagnetization components M_(x) and M_(y) meets an odd symmetry relationwith regard to x, whereas the other meets an even symmetry relation withregard to the x coordinate.

FIG. 7 shows a representation of a result of a numeric simulation whichis based on a magnetic body 110 comprising an extension of more than180° and being magnetized in the azimuthal direction, the magnitude ofthe magnetization being set to be constant across the volume of themagnetic body 110. In other words, the results of the simulation shownin FIG. 7 are based on an embodiment of a magnetic-field sensorcomprising a magnetic body 110 magnetized in the azimuthal direction ata constant magnitude, so that the magnetization again is inhomogeneousdue to the changing direction of same. Here, FIG. 7 again shows aplurality of field lines 230 as well as an arrow 240 in the inner partof the representation which corresponds to a direction along adecreasing magnetic flux density ranging from 0.5 T to 0.2 T, as is alsoindicted by the arrow 250. In addition, different lines 260 are againdrawn in FIG. 7, which relate to the curves 270 reproduced in FIGS. 8and 9. In other words, within the context of the following FIGS. 8 and9, suitability of the different lines 260 with regard to a potentialposition for the magnetic-field sensor elements 190 is examined.

FIG. 8 shows curves 270-1 to 270-8 of the x component of the magneticflux density Bx as a function of the x coordinate for different ycoordinates. More specifically, the curve 270-1 here corresponds to a ycoordinate of y=−0.8 mm, the y coordinate being reduced by 0.1 mm ineach case as numeral of the respective curve increases, the curve beingreproduced after the hyphen in the context of the reference numeral.Consequently, the curve 270-2 corresponds to a y coordinate of y=−0.9mm, and, for example, the curve 270-8 corresponds to a y coordinate ofy=−1.5 mm. Here, FIG. 8 initially shows the respective curves 270 on acoarse scale in a range from x=−2 mm to x=+2 mm, while FIG. 9 representsa magnification of the represented range from about x=1.0 mm to x=1.85mm.

Thus, FIG. 8 initially shows that almost independently of the yparameter selected in each case, in the range from about x=1.3 mm andx=1.4 mm, all curves 270 have an x component of the magnetic fluxdensity Bx which ranges from about +/−(20 mT-40 mT). At a smallerdistance from the magnet or magnetic body 110, i.e., for higher yvalues, the curves 270 in the range of around x=+/−1.4 mm run throughthe B_(x)=0 line, so that this may represent quite a suitable locationfor magneto-resistive sensor elements 190, i.e., GMR sensor elements190, for example.

Accordingly, in FIG. 9, the range of the curves depicted in FIG. 8 isrepresented in a magnified manner in the range of around x=1.4 mm. Forexample, FIG. 9 shows that in particular the curves 270-2, 270-3 and270-4, which correspond to the y parameters y=−0.9 mm, −1.0 mm and −1.1mm, intersect the “Bx=0” line in the range of around x=1.4 mm, as isshown by the detailed image in FIG. 9.

Before further embodiments of a magnetic-field sensor 100 will bedescribed in the context of FIGS. 10a and 10b , a short outline shall begiven of a method with which the inhomogeneous magnetizations discussedin the preceding figures may be realized. In the case of the magneticbodies 110 which comprise radial or quasi-radial magnetizations, as areshown, for example, in FIGS. 1a, 1b, 3a, and 3b , a counterpart which issuitably shaped and made of iron, for example, may be inserted into therecess 130 of the respective magnetic body, the counterpart seamlesslyadjoining the surface, suitably shaped, of the magnetic body 110. Also,an iron part, suitably shaped, may be placed into the outer surface fromthe outside, so that the future magnetic body 110 is covered byrespective iron parts from the outside and the inside. Subsequently, thetwo iron parts may be interconnected by a clamp which may take on almostany shape desired. A winding may be wound around the clamp, the windinghaving current applied thereto in order to generate the magnetization.

In the case of a magnetic body having an azimuthal magnetization, acircular conductor may be placed inside the magnet, i.e., into therecess 130 of the magnetic body 110, and a circular conductor may be fitsnuggly, ideally seamlessly, to the magnetic body 110 on the outside. Ifa current flowing in the inner metallic conductor is sent out of thedrawing plane drawn in FIG. 6a and FIG. 6b , respectively, and if in theouter conductor, a corresponding current is sent into the drawing plane,the respective magnetization within the magnet 110 will be aligned inthe azimuthal direction in an anticlockwise manner.

FIGS. 10a and 10b show further embodiments of a magnetic-field sensor300 differing from the above-shown embodiments of respectivemagnetic-field sensors 100 in that the embodiments shown here comprise afirst magnetic body 310 and a second magnetic body 320, the firstmagnetic body 310 comprising a first magnetization direction which ischaracterized by an arrow 330 in FIGS. 10a and 10b , respectively.Likewise, the second magnetic body 320 has a magnetization directionplotted by an arrow 340 in FIGS. 10a and 10b , respectively. The twomagnetization directions of the two magnetic bodies 310, 320 differ fromeach other and form an angle with each other.

With regard to a symmetry line 195, which again corresponds to an xcoordinate of x=0, the magnetization directions (arrows 330, 340) of thetwo magnetic bodies 310, 320 each form an angle with the symmetry line195 which is identical, in terms of magnitude, for the two magneticbodies 310, 320, or which does not deviate from one another by more thantypically 20°, 10°, 5° or 2°, depending on the specific implementationof a respective embodiment of a magnetic-field sensor 300 and itsspecifications. In other words, the two magnetic bodies 310, 320 in manyembodiments of a magnetic-field sensor 300 comprise a symmetricalmagnetization with regard to the symmetry line 195.

In addition, the embodiments of a magnetic-field sensor 300 depicted inFIGS. 10a and 10b again each comprise a magnetic-field sensorarrangement 120 having a substrate 180 and one or more magnetic-fieldsensor elements 190. As was already described in connection with theabove-explained embodiments of a magnetic-field sensor 100, themagnetic-field sensor arrangement may comprise a single magnetic-fieldsensor element 190 or a plurality of respective magnetic-field sensorelements 190. In the embodiments shown in FIGS. 10a and 10b , themagnetic-field sensor arrangement 120 in each case comprises twomagnetic-field sensor elements 190 arranged essentially symmetrically tothe symmetry line 195 which are manufactured by means of, for example,the potential magnetic-field sensor element technologies alreadydiscussed above. In this case, too, the magnetic-field sensor elementsmay include Hall sensor elements, magneto-resistive sensor elements, orother corresponding magnetic-field sensor elements.

It should be noted in this context that because of the above-describedproblems of the positioning tolerance in the case of realimplementations of embodiments of magnetic-field sensors 100, 300, theabove-described symmetry properties of the various components maydeviate, with regard to the symmetry line 195, only within a predefinedtolerance limit, i.e., for example, within a positioning tolerance,which is dependent on the application, in the lateral direction or inthe vertical direction. In other words, if the symmetry line 195 relatesto a center of, e.g., two magnetic-field sensor elements 190 on thesubstrate 180 of the magnetic-field sensor arrangement 120, the twomagnetic bodies 310, 320, which together form the back-bias magnet maypossibly deviate from their respective positions within predefinedpositioning tolerances. In many cases, the respective positioningtolerances are application-specific and are certainly influenced, forexample, by the technology of the magnetic-field sensor elements 190used.

In addition, a generator object 210 is again drawn in FIGS. 10a and 10b, the generator object 210 again being, for example, a rack, a magnetrod, a drilled rod, a toothed wheel, a drilled wheel, or a magnet wheel.Depending on the specific application, other generator objects 210 mayalso be employed, it possibly being useful in many cases, depending onthe specific implementation, to configure the respective generatorobject 210 such that it is able to cause a modulation, for example, aperiodic or sinusoidal modulation, of a magnetic field which (amongothers) is generated, in this case, by the first magnetic body 310,frequently configured as a permanent magnet, and the second magneticbody 320 of the back-bias magnet arrangement, or of the back-biasmagnet.

With respect to the symmetry line 195, in many embodiments of amagnetic-field sensor 300, the first magnetic body 310 and the secondmagnetic body 320 are configured, or arranged, to be symmetrical tosame. In addition to the above-mentioned possibility of performing adefinition of the symmetry line 195 with regard to a central position ofmagnetic-field sensor elements 190, if same are present in acorresponding number and layout, there is naturally also the possibilityof defining the symmetry line 195 with regard to a central point or anyother corresponding line or mark with respect to the substrate 180.While taking into account the positioning deviations or positioningtolerances of the individual magnetic bodies 310, 320 which are caused,for example, by manufacturing tolerances, they each have a symmetricalinstallation position with regard to the symmetry line 195.

As was explained before, depending on the specific definition of thelocation of the symmetry line 195, the two magnetic bodies 310, 320and/or the locations of the individual magnetic-field sensor elements190 may comprise corresponding installation tolerances or positioningtolerances with regard to the symmetry line 195. In other words, acenter of gravity of the two magnetic bodies 310, 320 may be spacedapart from the symmetry line 195 by a distance typically smaller than acorresponding positioning tolerance.

The same applies not only in the x direction, but also in the ydirection, which is perpendicular thereto, as is drawn in FIGS. 10a and10b . Depending on the production technology used, in particular on thetechnology of securing the magnetic bodies with regard to themagnetic-field sensor arrangement 120, positioning errors ranging fromseveral 100 μm to several millimeters thus cannot occur in the xdirection and/or y direction as well as in the z direction, which is notshown in FIGS. 10a and 10b . In other words, the respective positioningtolerances may be in the range of up to several 100 μm, or in the rangeof up to several millimeters, i.e., in the range of up to about 1000 μm,or in the range of up to about 2 mm.

With regard to the positioning of the individual magnetic-field sensorelements 190 in relation to one magnetic body, respectively, of the twomagnetic bodies 310, 320, in many embodiments of a respectivemagnetic-field sensor 300, provided that the magnetic-field sensorelements 190 and/or of the magnetic bodies 310, 320 are arrangedsymmetrically, the magnetic-field sensor elements 190 each comprise xcoordinates within the range of the x coordinates of one of the twomagnetic bodies 310, 320. In other words, in such embodiments of amagnetic-field sensor 300, the associated magnetic-field sensor elements190 are located above or below the respective magnetic bodies 310, 320.

With respect to the angles formed by the magnetization directions of theindividual magnetic bodies 310, 320 and the symmetry line 195, or theline 350 extending perpendicular to same and also drawn in FIGS. 10a and10b , in many embodiments of a magnetic-field sensor 300, an angle ofthe magnetization of one of the two magnetic bodies 310 in many casesforms an angle of between 10° and 80° in terms of magnitude with thesymmetry line 195. In many embodiments of a magnetic-field sensor 300,the symmetry line 195 runs perpendicular to a main surface or surface ofthe substrate 180 having the magnetic-field sensor elements 190 arrangedthereon. Accordingly, the respective magnetizations also form an angle,with regard to the line 350, ranging from 10° to 80° in terms ofmagnitude. In addition, in the case of a symmetric design of the twomagnetic bodies 310, 320, the respective magnetizations in each caseform an angle with each other which ranges from 20° to 160° in terms ofmagnitude. Depending on the specific field of application, other rangesof angles, which shall be explained in more detail in the further courseof the present application in the context of numeric simulations, mayalso occur in embodiments of a magnetic-field sensor 300.

The embodiments of a magnetic-field sensor 300 depicted in FIGS. 10a and10b differ essentially with respect to the arrangement of the twomagnetic bodies 310, 320 in relation to each other. While in theembodiment shown in FIG. 10a , the two magnetic bodies 310, 320immediately adjoin each other, for example, in that they are fixed toeach other by means of gluing, in the embodiment shown in FIG. 10b , thetwo magnetic bodies 310, 320 are separated from each other by arespective gap. The gap between the two magnetic bodies 310, 320 may befilled, for example, with a magnetic or non-magnetic material, whichserves, for example, for attachment or serves the overall architectureof the embodiment of a magnetic-field sensor 300. For example, a plasticattachment may be partly or fully inserted between the two magneticbodies 310, 320, to which plastic attachment the two magnetic bodies310, 320 are glued or otherwise attached. Alternatively or additionally,the two magnetic bodies 310, 320 may also be fixed to one another withinthe framework of the overall installation of the magnetic-field sensorarrangement 120, so that encapsulating material at least partly entersinto the gap between the two magnetic bodies 310, 320.

As was already set forth in the context of the embodiment shown in FIGS.3a, 3b of a magnetic-field sensor 100, in embodiments of amagnetic-field sensor 300, too, the magnetic-field sensor arrangement120 with its substrate 180 and the magnetic-field sensor elements 190may, for its part, comprise a package.

Of course, it is also possible, in principle, that no solid material isinserted between the two magnetic bodies 310, 320, as is shown in FIG.10b , but that rather the two magnetic bodies 310, 320 are directlyconnected or glued to the magnetic-field sensor arrangement 120. In sucha case, introducing a material between the two magnetic bodies 310, 320may possibly be dispensed with.

In the embodiments of a magnetic-field sensor 300 which are shown inFIGS. 10a and 10b , two individual magnets as magnetic bodies 310, 320are assembled to form a new magnet or back-bias magnet such that, again,the symmetry conditions given in equation (1) apply to the magnetizationcomponents of the overall arrangement of the two magnetic bodies. This,too, again corresponds to an inhomogeneous (bulk) magnetization withrespect to the overall arrangement of the two magnetic bodies 310, 320.More specifically, this corresponds to an inhomogeneously magnetizedbulk magnet, each half of the volume of which consists of onehomogeneously magnetized magnetic body, or one homogeneous area,respectively. In FIGS. 10a and 10b , in the embodiments of amagnetic-field sensor which are shown there, a second cube is joinedwith an oblique magnetization, respectively, as possibly the simplestexample.

Depending on the specific implementation, for example, the two magneticbodies 310, 320 may be configured as two block magnets having a width ofabout 2 mm and a height of about 5 mm, and may be bonded to one anotherback to back. Both individual magnetic bodies 310, 320 in this contextare homogeneously magnetized, a remanence of about Brem=1 T prevailingin the respective direction shown by the magnetization, or the arrows330, 340, again depending on the specific implementation. In someembodiments, the magnetization direction may comprise, for example, anangle of +/−50° with respect to the symmetry line 195, i.e., to thevertical direction.

Some embodiments of a magnetic-field sensor 300, which correspond to thearrangements of FIGS. 10a and 10b , provide very good results withregard to a combination with a magnetic-field sensor arrangementcomprising magneto-resistive sensor elements. In addition, they mayfrequently be manufactured in a particularly simple manner since therespective magnetic bodies 310, 320 as homogeneously magnetizedindividual magnets may be manufactured in a comparatively simple manner.

As it was the case already in the context of the embodiments of amagnetic-field sensor 300 which are shown in FIGS. 3a and 3b , it mayalso be useful in this case, depending on the specific implementation,to implement the magnetic-field sensor arrangement 120 such that it ismirrored with respect to the line 350, so that the magnetic-field sensorelements 190 in connection with the finished magnetic-field sensor facethe generator object 210.

As is schematically depicted in FIG. 10b , the two magnetic bodies 310,320 may also be spaced apart from each other by a non-magnetic gap.Depending on the specific implementation, this may be helpful ininstallation, for example, since a corresponding distance may beconfigured as an adhesive surface. In addition, there is also thepossibility of influencing an interaction of the two magnetic bodies310, 320 by introducing such a non-magnetic gap, so that they may notsuperimpose or influence each other to such a large degree.

Thus, some embodiments of a magnetic-field sensor 300 with regard to theback-bias magnet formed by the two magnetic bodies 310, 320 are based onthe idea that when the field lines of a magnet diverge, a second magnetmay be arranged next to it, the second magnet canceling out theundesired components of the first magnet.

FIG. 11 shows a result of a numeric simulation of a magnetic fluxdensity distribution of an embodiment of a magnetic-field sensor 300 asis schematically shown in FIG. 10a . In addition to a number of fieldlines 230, FIG. 11 shows a magnetic flux density distribution calculatedin the area of the two magnetic bodies 310, 320 and ranging from 0.2 to0.5 T. As is already schematically shown in FIG. 10a , the two magneticbodies 310, 320 have a magnetization having a magnetic remanence ofBrem=1 T, which is also indicted by the arrows 330, 340 in FIG. 11. Themagnetic flux density distribution resulting therefrom is reproduced inaccordance with the gray scale distribution depicted in FIG. 11, amaximum magnetic flux density prevailing at a contact area of the twomagnetic bodies 310, 320, while a magnetic flux density clearly smallerthan same prevailing outside the two magnetic bodies 310, 320.

In addition, FIG. 11 depicts a line 260, with respect to which FIG. 12ashows an x component of the magnetic flux density Bx in a range fromx=−2 mm to x=+2 mm for a y coordinate of y=−1 mm. Here, the numericsimulation shown in FIG. 11 is based on two cubic magnets or magneticbodies 310, 320 each having a homogeneous magnetization which, however,forms an angle of +/−35° with the y or By axes extending verticallydownward. Consequently, there is an angle of 55°, in terms of magnitude,between the two magnetizations of the two magnetic bodies 310, 320 andthe horizontal.

As was briefly indicated above, FIG. 12a shows the x component Bx as afunction of the x coordinate for a y value of y=−1 mm, which correspondsto the line 260 shown in FIG. 11. Subsequently, FIG. 12b shows thecorresponding x components of the magnetic flux density Bx as a functionof the x coordinate foray value of y=−1.5 mm, which is not drawn in FIG.11, however.

In the event of a y value of y=−1 mm, FIG. 12a shows the x component ofthe magnetic flux density Bx in the range from x=−2 mm to x=+2 mm forvarious angles of the magnetizations of the two magnetic bodies 310,320. Here, the simulations are based on the above-explained symmetry ofthe magnetization directions of the two magnetic bodies 310, 320, eachof which forms an angle, in terms of magnitude, with the horizontal ineach case, the angles being reproduced using the reference numerals ofthe individual curves 270. The curve 270-70 is based on an angle of 70°of the magnetizations of the two magnetic bodies 310, 320 with thehorizontal, so that for this simulation or calculation, themagnetizations of the two magnetic bodies form an angle of 20° with thesymmetry line 195 of FIG. 10a . Accordingly, the curve 270-55corresponds to the case shown in FIG. 11 of an angle of 35° between thevertical symmetry line 195, or to an angle of 55° of the magnetizationand the horizontal.

Accordingly, FIG. 12b shows several curves 270 for angles ranging from40° to 70°, which are formed by the magnetizations of the two magneticbodies 310, 320 and the horizontal. Consequently, the curves 270-40 to270-70 depicted in FIG. 12b correspond to angles ranging from 20° (curve270-70) to 50° (curve 270-40) of the magnetizations of the magneticbodies 310, 320 with respect to the vertical symmetry line 195 shown inFIG. 10a . Especially in the case, shown in FIG. 12b , of a verticaldistance of 1.5 mm of the magnetic-field sensor elements 190 from thelower edge of the two magnetic bodies 310, 320 (y=−1.5 mm; the magnetends at y=0 mm), it may be seen that the condition |Bx|<20 mT may be metfor further ranges of the x coordinates in the case of y=−1.5 mm. Sincethis may also be met for the case shown in FIG. 12a in the range offurther x coordinates, there is thus the possibility, in particular, ofimplementing magneto-resistive magnetic-field sensor elements 190 usingan embodiment of a magnetic-field sensor 300 as is schematically shown,for example, in FIG. 10a or 10 b, without the magnetic-field sensorelements 190 being driven into saturation by the respective x componentsof the magnetic fields caused by the magnetic bodies 310, 320.

In other words, using an embodiment of a magnetic-field sensor 300, ahorizontal component of a magnetic flux density (for example, xcomponent) Bx may be created within a comparatively wide range of x andy coordinates, the component not causing a saturation ofmagneto-resistive sensor elements 190. In the case of GMR sensorelements, FIGS. 12a and 12b thus show that a condition |Bx|<20 mT, whichapplies to many GMR sensor elements, may be met for wide ranges of x andy coordinates.

In addition, FIGS. 12a and 12b show that by varying the directions ofthe two magnetic bodies 310, 320, the respective ranges may be shiftedsuch that different distances may be realized between magnetic-fieldsensor elements 190. Thus, it is possible to provide differentembodiments of magnetic-field sensors 300 having different mutualdistances of the magnetic-field sensor elements 190.

In summary, one may state that by using corresponding embodiments ofmagnetic-field sensors 300 comprising (at least) two magnetic bodies310, 320, magnetic systems may be built, so that the respectivemagnetic-field sensor elements 190 are not driven into saturation evenin the case of sensitive magneto-resistive sensor elements, i.e., GMRsensor elements, for example.

FIG. 13 shows a further embodiment of a magnetic-field sensor 300 whichdiffers from the embodiments, shown in FIGS. 10a and 10b , of amagnetic-field sensor 300 essentially in that the two magnetic bodies310, 320 no longer comprise, with respect to their geometric shapes, anoblique magnetization, but rather are perpendicularly magnetized withrespect to a front face. In this case, the two magnetic bodies 310, 320are no longer arranged in parallel with respect to their side faces, aswas the case in the embodiments in FIGS. 10a and 10b . Rather, in orderto achieve the two different magnetization directions of the twomagnetic bodies 310, 320, they are now arranged, for their part, at arespective angle with respect to the symmetry line 195 or to the line350 perpendicular to same.

Thus, in this case, too, the first magnetic body 310 and the secondmagnetic body 320 comprise differing first and second magnetizationdirections, respectively. Thus, an inhomogeneous bulk magnetization isachieved, also in the case of such an arrangement of magnetic bodies310, 320, by superimposing the magnetic fields of the two (homogeneouslymagnetized) magnetic bodies 310, 320.

In other words, respective arrangements of magnetic bodies 310, 320comprising different magnetization directions, respectively, may befound by employing two cubic magnets or magnetic bodies which aremagnetized in the longitudinal direction and are implemented andinstalled such that they are tilted by a respective angle, e.g., +/−35°,relative to the y axis, instead of using two slanted or obliquemagnetized magnetic bodies 310, 320. In other words, for embodiments ofmagnetic-field sensors 300 it is irrelevant whether the two differentmagnetization directions of the two magnetic bodies 310, 320, as arerepresented by the arrows 330 and 340, are created by using magneticbodies comprising different, slanted magnetizations, or whether magneticbodies comprising identical magnetizations are employed, which, however,are built in an accordingly slanted manner or using correspondinginstallation directions within the context of the respective embodimentof the magnetic-field sensor 300.

With regard to the more specific installation positions of theindividual magnetic bodies 310, 320 in an embodiment as is depicted inFIG. 13, the above explanations shall also apply, of course, the onlydifference being, in this case, that the respective magnetic bodies 310,320 now is rotated accordingly.

Actually, there is a very large degree of freedom with regard to thespecific shapes of the individual magnetic bodies 310, 320. Inprinciple, any shapes conceivable of respective magnetic bodies may beused. For example, cubic, cylindrical and other magnetic bodies, forexample, magnetic bodies which taper off, are feasible. In addition, ofcourse, not only homogeneously magnetized magnetic bodies may be used inthe context of the two magnetic bodies 310, 320, as was implicitlyassumed in the embodiments previously described, but use may naturallyalso be made of inhomogeneously magnetized magnetic bodies. In otherwords, the magnetic bodies 310, 320 may also be implementedinhomogeneously with regard to their magnetization directions and theirmagnetization intensities.

Embodiments of magnetic field sensors 100, 300 thus enable to reducehorizontal magnetic-field components, or horizontal components, of themagnetic flux density by using inhomogeneous magnetization of themagnetic body 110, or of the back-bias magnet, the latter including atleast the two magnetic bodies 310, 320, to such a degree that, forexample, magneto-resistive sensors (xMR sensors) are no longeroverdriven, i.e., driven into saturation. As was already explainedabove, embodiments of magnetic-field sensors 100 therefore enable toreduce the flux density component, which in the context of the presentapplication is casually also referred to as the Bx field of theback-bias magnet, by means of the inhomogeneous magnetizations describedto such a degree that respective overdriving of the sensors or sensorelements will not occur.

Embodiments of the present invention in the form of magnetic-fieldsensors 100, 300 achieve a field line curve desired in that, among otherthings, the respective components of the resulting magnetic flux densityare limited by an inhomogeneous magnetization of the magnetic bodies110, 310, 320. Accordingly, embodiments of magnetic-field sensors 100,300 may possibly also be produced without implementing magnetic bodieswith extremely filigree shapes or recesses, or respective embodiments ofmagnetic-field sensors 100, 300 may possibly also be developed and builtwithout using highly permeably parts as magnetic lenses for field-linedeformation. Embodiments of respective magnetic-field sensors 100, 300may be used, among other things, for magneto-resistive speed sensorswhile employing respective back-bias magnet circuits in the form of themagnetic bodies 110, 310, 320. Examples of use of respective embodimentsof magnetic-field sensors are found in the automobile sector as well asother sectors, such as mechanical engineering, plant engineering,aircraft construction, shipbuilding, and other fields of technologywhere magnetic fields need to be detected.

FIG. 14A illustrates a cross-sectional view of a further embodiment ofan inhomogeneous magnet 400 suitable as a back-bias magnet to be used incombination with magnetic sensor 120 as discussed above. Theinhomogeneous magnet 400 is somewhat similar to the magnet 110, or themagnetic bodies 310, 320. It is to be noted however that theinhomogeneous magnet 400 does not comprise two distinct magnetic bodiesof substantially homogeneous magnetization that are joined together ormeet under a specific angle leading to the above described degree ofinhomogeneous magnetization. To the contrary, the inhomogeneous magnet400 is moldable as a unitary member, yet comprising the inhomogeneousmagnetization as indicated by the arrows 14-1, 14-2, 14-3 representing adirection of magnetization at a certain position within thecross-sectional view of the magnet 400. The cross sectional view of FIG.14A is shown along the x-z plane this is to say a B_(x) component of themagnetization is indicated at the bottom of the figure, while a B_(z)component of the magnetization is indicated to the left side of thefigure. It will be appreciated that this choice serves illustrativepurposes and the magnet 400 may comprise an inhomogeneous magnetizationwithin other cross-sections instead. The magnetization illustrated inFIG. 14A is depicted symmetrical to a symmetry line 14-0 as representedby the dot dashed line.

While the inhomogeneous magnetization of FIG. 14A is illustrated asbeing fully symmetrical to the symmetry line 14-0, it will beappreciated that for a real cross-section of the inhomogeneous magnet400 various effects may break symmetry of the magnetization within thecross-section, so that this magnetization is no longer fullysymmetrical. Such effects may be faces limiting the magnet 400,(magnetic) impurities within the magnet 400, and/or magnetic substancessufficiently close to the magnet but are not limited thereto. For thepresent disclosure a magnetization shall be considered symmetricalwithin a cross-section even if only 90%, 80% or 50% of thecross-sectional area in fact exhibit a symmetrical magnetization withregards to the symmetry line 14-0 within the cross-section.

For this disclosure the magnetization (as illustrated in FIG. 14), it isto be understood that this symmetry line 14-0 may be indicating a mirrorsymmetrical magnetization of the magnet 400. Without limitation thesymmetry line 14-0 as indicated in the cross-section of FIG. 14A, may beindicating higher order symmetry of the magnet 400, say a three-fold orhigher order of symmetry. An object of higher order of symmetrycomprises more than one cross-sectional plane to which or within whichsome properties of the object are symmetrical, say for example amagnetization of the object or crystal structure of a mineral. So for ahigher order symmetry line there may more than one cross-section presentto which or within which the property of the symmetrical object issymmetrical, while the more than one cross-sections actually intersectat the higher order symmetry line.

It will further be appreciated that the symmetry line 14-0 of the magnet400 as displayed in FIG. 14A may in fact be indicating a rotational oran ellipsoidal symmetry axis. So a person of ordinary skill will readilyappreciate that the back-bias magnet 400 may also be of rotationalsymmetry. Therefore, any disclosure pertaining to the inhomogeneous(back-bias) magnet, such as back-bias magnet 400, may be transferred toobjects of rotational symmetry. A rotational or ellipsoidal symmetry ofthe magnet may be of interest depending on circumstances. It will beappreciated that an ellipsoidal symmetry axis corresponds to arotational symmetry with not just one radius but a rotation between afirst and a second radius yielding an overall ellipsoidal characteristicwhen viewed in a cross-section substantially perpendicular to thesymmetry line 14-0.

As before a magnetization of higher order symmetry, rotational symmetry,or ellipsoidal symmetry within a cross-section shall still be consideredsymmetrical to the higher order symmetry, rotational symmetry, orellipsoidal symmetry, even if only 90%, 80% or 50% of thecross-sectional area in fact exhibit a magnetization of higher symmetrywith regards to the symmetry line 14-0. Similarly, the magnetization ofthe back-bias magnet shall be considered of higher order symmetry,rotational symmetry, or ellipsoidal symmetry, even if only 90%, 80% or50% of the volume of the magnet in fact exhibit a magnetization ofhigher symmetry with regards to the symmetry line 14-0.

It will be noted that at a lower portion of the cross-sectional view(lower or zero z values) the magnetization of the magnet 400 is almostcompletely aligned along the z axis. With increasing z coordinatehowever the magnetization is increasingly inhomogeneous. This is to saythe higher the z coordinate the larger is an angle α between the zdirection and the orientation of the magnetization as may be seen fromFIG. 14A when comparing the angle α for increasing z coordinates.Obviously the magnetization is aligned parallel along the symmetry axis140-0. When walking parallel to the symmetry line 14-0 but not on thesymmetry line, which would be in the z direction for a given xcoordinate, the angle α will substantially increase with increasing zvalues. Such a behavior may be referred to as monotonic, more preciselymonotonically increasing.

If one was to walk along a path perpendicular to the symmetry line 14-0one may experience a non-monotonic behavior of the angle α. This is tosay when walking parallel to the symmetry line 14-0, the angle α mayfirst decrease until the symmetry line 14-0 is reached and will increaseagain after having passed the symmetry line. Walking perpendicular tothe symmetry line 14-0 would correspond in FIG. 14A to walking in xdirection for a given z value along the cross section.

Likewise, the angle α of the magnetization increases when walking awayfrom the symmetry line in a horizontal direction (constant z coordinate)for those portions of the magnet 400 that are not at the lower part ofFIG. 14. The increasingly inhomogeneous magnetization is best seen whencomparing the angle α for arrows 14-1, 14-2, and 14-3. An alternativeway of describing the increasingly inhomogeneous magnetization whenwalking along the z direction (except along the symmetry line 14-0) isto call it increasingly divergent. It will be appreciated that thecross-sectional distribution of magnetization serves for illustrativepurposes, only and not to limit the teaching of the present disclosurein any way.

A person of ordinary skill will appreciate that it is feasible toproduce a bulk magnet comprising an inhomogeneous magnetization asillustrated in FIG. 14A using a mold process. According to a firstvariant of such molding process, and somewhat similar to the discussionwith regards to a production of radially magnetized magnets (FIG. 3a, 3brespectively), the molding tool may be configured to generate aspatially varying magnetic flux density inside the tool whilemagnetizable molding material is injected into and/or melted inside themolding tool. The spatially varying magnetic flux density inside themolding tool will project onto the magnetizable molding material andshall persist once the molding process is completed yielding the bulkmagnet 400 with inhomogeneous magnetization as a unitary member. In factmolding tool, magnetizable molding material and spatially varyingmagnetic flux density inside the tool may be selected to virtuallyachieve any desired spatially varying magnetic flux density inside themagnet 400 once the molding process is finished.

It will be appreciated that an alternative molding process may be usedto produce a bulk magnet comprising an inhomogeneous magnetization asillustrated in FIG. 14A. The molding tool may be filled with a standardmagnetizable or magnetic molding material and may harden in the desiredform of the inhomogeneous magnet to be produced. It is conceivable thatduring the hardening of the inhomogeneous magnet to be produced noexternal magnetic field or a homogeneous external magnetic field may beapplied. This would lead to a magnet showing a moreless vanishingmagnetization or a uniform magnetization. Once the magnetizable moldingmaterial is hardened, an inhomogeneous external magnetic field may beapplied to the hardened molding material in the shape of theinhomogeneous magnet to be produced. It may be of advantage to apply theinhomogeneous magnetic field to the hardened molding material while itis still in the molding tool. Such an approach may be of advantage asthe inhomogeneous magnet 400 leaves the molding tool. As a trade-offtime required per unit inside the molding tool may be increased withthis approach. Depending on circumstances it may however be of interestto move the hardened molding material in the shape of the inhomogeneousmagnet into a magnetization device providing a sufficiently largeinhomogeneous magnetic field to project onto the magnetizable hardenedmolding material in the shape of the inhomogeneous magnet; therebycompleting manufacture of the inhomogeneous magnet 400 according to thepresent disclosure.

FIG. 14B illustrates an exemplary shape of the inhomogeneous magnet 400according to the present disclosure. It may be convenient to provide themagnet 400 in a brick-type, i.e. cuboidal shape or slightly taperedbrick-type shape, as displayed in FIG. 14B. Such a shape may be ofinterest in order to replace known back-bias magnets with theinhomogeneous magnet 400 being moldable. A back-bias magnet supplierwould typically overmold the back-bias magnet 400 and the sensorarrangement 120 (not shown) in order to build a module that is sold onto a client of the supplier, the module now comprising communicationmeans from the sensor elements to an ECU, which are not discussed withregards to this disclosure in detail.

Without limitation the sensor 100 (see FIG. 2) built by the automotivesupplier may as well have a brick-type shape as shown in FIG. 14B, whilecommunication means form the sensor elements to the ECU are not shown.The sensor 100, too may have a shape of rotational symmetry orellipsoidal symmetry. The sensor 100 of the rotational or ellipsoidalsymmetry may optionally take a frustum shape, depending oncircumstances. A person of ordinary skill will understand that anellipsoidal shape of the sensor 100 may have the advantage that arotation of the sensor 100 upon installation is easily prevented just bysome housing provided within the vehicle matching the ellipsoidal shapeand thereby arranging the sensor 100 in an intended position.

If the sensor 100 was however of a rotational symmetry one may provide agroove or a notch at a face of the sensor in order to provide anarranging of the sensor as is achievable for the ellipsoidal shape. Itmay be of advantage to arrange the groove or notch away from themagnetic-field sensor arrangement 120, in order for the groove or notchnot to affect a magnetic field distribution close to the magnetic-fieldsensor arrangement 120 (not shown).

FIG. 14C illustrates such a shape for the sensor 100 comprising a groove101 away from the sensing elements 190. Such a notch may mate with aprotrusion within the housing for the sensor 100 provided in a deviceusing the sensor, such as a vehicle. As an alternative to the notch, afrustum shaped sensor 100 may comprise non-parallel top and bottom faces(more generally speaking non-parallel non-circumferential faces) so thatthe sensor 100 will only mate with a corresponding housing in a definedcircumferential position. Other options of positioning the sensor 100 ofrotational symmetry within the corresponding housing will be apparent toperson of ordinary skill in the art and shall therefore not be explainedany further here.

FIG. 14C discloses a further alternative of implementing the sensor 100.In the implementation of FIG. 2 the sensor elements 190 are arranged ina sensor package forming the magnetic-field sensor arrangement 120.Unlike in FIG. 2, the sensor 100 of FIG. 14C does not comprise thepackage forming the magnetic-field sensor arrangement 120. It will benoted that one packing/molding step may be spared by implementing thesensor 100 using a bare-die chip 195 carrying the sensor elements 190without the package. Such an implementation of the sensor 100 will bemore cost-efficient for the (automotive) supplier. As a trade-off careneeds to be taken that the sensing elements 190 and consequently thebare-die chip 195 are spatially correctly arranged with regards to theback-bias magnet 400. While their correct alignment in the previousimplementations of the sensor 100 was catered for by the chipmanufacturer, the correct alignment would now be a task left to thesupplier.

While there is a spatial distance between the bare-die chip 195 and theback-bias magnet 400 in FIG. 14C, it will be appreciated, that theinhomogeneous magnetization of the back-bias magnet 400 may be designedsuch that the bare-die chip 195 can be directly placed onto theback-bias magnet 400. A person of ordinary art will appreciate that thebare-die chip 195 typically requires some coupling means in order toprovide an electrical communication from the bare-die chip 195 to anoutside thereof. Such means of providing electrical communication may bein the form of a lead frame, but are not limited thereto. A person ofordinary skill will appreciate other options for providing theelectrical communication, which are not limiting the teaching of thepresent disclosure and are therefore not described in further detail.For the remainder of the present disclosure bare-die chip 195 shall beconstrued as optionally comprising the coupling means. In variousembodiments, the bare-die chip 195 design of the back-bias magnet 400facilitates the correct spatial arrangement of the bare-die chip 195relative to the back-bias magnet 400.

FIG. 14D illustrates a further alternative of implementing the sensor100 comprising the back-bias magnet 400. In fact, for the implementationof FIG. 14D, the inhomogeneous magnet 400 also serves as the housing ofthe sensor 100. By appropriately controlling both spatial distributionof the inhomogeneous magnetization of the magnet 400 and the positioningof the bare die chip 195 relative to the inhomogeneous magnetization,the package covering the sensing elements 190 and the further moldingmaterial providing the housing may be spared. In FIG. 14D the spatialdistribution of magnetization is substantially symmetrical to thesymmetry line 14-0, showing different degrees of inhomogeneity 14-1,14-2, 14-3 pertaining to the angle α as was explained with regards toFIG. 14A.

It will be appreciated that the inhomogeneous magnet 400 is of advantagewhen used together with a magnetic-field sensor arrangement 120 as lessmagnetic material is required in order to achieve a comparableinhomogeneous magnetic flux density at the sensor elements 190. This isdue to the fact that the magnet 400 (see FIG. 14A, C, D) may be arrangedcloser to magnetic-field sensor arrangement 120, wherein say first andsecond sensor elements 190-1, 190-2 (see FIG. 2, 14C, 14D) are placed,than for magnet arrangements not having a convex shape as the magnet400.

As a further benefit of the magnet 400 the sensor 100 and/or the magnet400 require less space than would those systems comprising non-convexmagnets (such as for example magnet 150 of FIG. 1A, magnet 110 of FIG.3A, 3B, 6A, or 6B). In spatially constrained environments such as motorspace of a combustion engine in the automotive arena smaller size of theback-bias sensor system is of interest.

It is to be noted that a moving target wheel rotating in direction 220is shown for illustrative purposes only in FIGS. 14C and 14D and doesnot form part of the described (back-bias) sensor 100.

It will be appreciated by a person of ordinary skill in the art that theinhomogeneous magnet 400 may be formed using hard ferrite material orrare earth materials as magnetizable molding material, such as ferrites,aluminum-nickel-cobalt (AlNiCo), or samarium-cobalt (SmCo) orneodymium-iron-boron (NdFeB), to name some non-limiting examples,respectively.

Generally, hard ferrite magnets are cheaper than rare-earth basedmagnets which as such would reduce magnet costs, however hard ferritemagnets have a weaker magnetic moment therefore will produce a weakerhomogeneous magnetic fields for homogeneous magnets of identical sizewhen compared to rare-earth based magnets. In order to compensate forthis tradeoff, the use of inhomogeneous hard ferrite magnets accordingto the present disclosure helps increasing their respective magneticfield matching the magnetic field strength of rear earth magnets at thecost-benefit of hard ferrite magnets. In the pasta rare earth magnetswere conveniently used for the non-convex magnets described above (seefor example magnet 150 of FIG. 1A, magnet 110 of FIG. 3A, 3B, 6A, or6B). Therefore the inhomogeneous magnet 400 employing hard ferritematerials comes with further advantage over non-convex magnets made ofrare earth magnet materials, such as samarium-cobalt (SmCo) orneodymium-iron-boron (NdFeB).

FIG. 15 schematically illustrates the B_(x) component relative to thesymmetry line of a magnet (x=0) for a given y coordinate. In thisrespect the illustration of FIG. 15 somewhat corresponds to the scenariodepicted in FIG. 5 as explained above. It becomes apparent that whilethe B_(x) component for an homogeneous magnet (see solid line 15-3) isof odd symmetry with regards to x=0, the B_(x) component for aninhomogeneous magnet (say magnet 400 as discussed above) is almostvanishing over a substantial range of x-coordinates, as can be seen fromthe long dashed line 15-4. The short dashed lines 15-1 and 15-2 indicatetypical positions for magnetoresistive sensors, such as GMR sensingelements.

As discussed before with regards to curve 270-6 (see FIG. 5), the B_(x)component of the inhomogeneous magnet 400 shows an increased linearrange and would therefore represent a preferred position for GMR sensorelements. The magnetic-field sensor elements 190 (i.e. FIG. 2) couldconveniently be positioned symmetrically about x=0 as indicated byposition lines 15-1, 15-2, respectively, over a wider x range than forthe homogenous magnet (see line 15-3 of FIG. 15). In FIG. 15 for thesimulated magnetic field components for the homogeneous andinhomogeneous magnet (see lines 15-3 and 15-4) a distance of the sensorplane with the sensor elements is 0.7 mm above the magnet in zdirection. As indicated the sensor elements show a sensor pitch ordistance of 2.5 mm in x direction.

FIG. 16 illustrates a 3D plot of an exemplary simulation ofmagnetization for the inhomogeneous magnet 400 of FIG. 14 using astandard polymer-bound hard ferrite molding material. These moldingmaterials typically show a remanence magnetic field of about 270-280 mT,and a corresponding coercitivity of 180 kA/m. As can be clearly seen aspatial distribution of the magnetization within the magnet 400 isinhomogeneous, as was already schematically discussed with regards toFIG. 14A. The color coding as indicated on the scale to the right ofFIG. 16 illustrates a strength and direction of magnetization. It willbe appreciated the magnetization of the inhomogeneous (back-bias) magnet400 will provoke a magnetic flux density outside the magnet 400,different to so called Halbach magnet arrangements which representmagnet configurations with virtually all magnetic flux density confinedinside the Halbach magnet. Such a confinement of magnetic flux to theinside of the magnet, would with non-Halbach magnets be achievable, ifthe magnet would be infinitely long, high, and/or wide. Also from FIG.16, a person of ordinary skill in the art will readily appreciate thatvirtually any desired inhomogeneous distribution of magnetization withinthe magnet 400 may be generated, as was explained already above.

FIG. 17 illustrates further details taken from the simulation of FIG.16. Displayed is the simulated B_(x) component in mT of the magneticfield produced by the magnet 400 centered at the symmetry line (see 14-0of FIG. 14) for realistic distances of the sensor elements from thesurface of the magnet 400 in y and z direction, respectively. Theassumed distances are 0.7 mm in z direction and a central placement iny-direction (y=0 mm).

Line 17-1 illustrates the B_(x) component for a substantiallyhomogeneous magnet, while lines 17-2, 17-3, and 17-4 show the B_(x)component for an increasingly inhomogeneous magnet 400. The increasinginhomogeneity shown for lines 17-2, 17-3, and 17-4 may be represented byan increasing angle α (see FIG. 14) associated with line 14-0 to 14-1,14-2, and 14-3. As already discussed for FIG. 15 the increasinglyinhomogeneous magnetization as shown in FIG. 17 for lines 17-2, 17-3,and 17-4, increases a linear range of the magnetoresistive sensorelements 190 (not shown) to be placed in x direction as indicated by thedotted lines 15-1, 15-2, respectively.

As the B_(x) component for the strongest inhomogeneity represented byline 17-4, almost vanishes at the sensor positions 15-1, 15-2,respectively, this amount of inhomogeneity of the B_(x) component wouldmake the sensor positions 15-1, and 15-2 ideal positions for placing thesensor elements in the x direction, as was described before with regardsto FIG. 5.

It will be appreciated by a person of ordinary skill in the art that thepresent disclosure depicts inhomogeneous magnetization of the magnet 400(see FIG. 1A, 1B, 3A, 3B, 4-14, 14A, 14D, 15-17) within cross-sectionsof the inhomogeneous magnet, such as the xy or xz plane, only, forillustrative purposes. The inhomogeneous magnet of the presentdisclosure is however in no ways limited to such a scenario. The magnetmay therefore comprise further inhomogeneous magnetization contributionswithin further cross-sections of the magnet, the further cross-sectionsbeing perpendicular to those depicted in the Figures of the presentdisclosure.

Depending on the conditions, embodiments of the inventive methods may beimplemented in hardware or in software. Implementation may be performedon a digital storage medium, in particular a disk, CD or DVD comprisingelectronically readable control signals which may cooperate with aprogrammable computer system such that an embodiment of an inventivemethod is performed. Generally, an embodiment of the present inventionthus also consists in a software program product, or a computer programproduct, or a program product, comprising a program code, stored on amachine-readable carrier, for performing an embodiment of an inventivemethod, when the software program product runs on a computer or aprocessor. In other words, an embodiment of the present application maythus be realized as a computer program, or a software program, or aprogram comprising a program code for performing an embodiment of amethod, when the program runs on a processor. The processor may beformed by a computer, a chip card (smart card), a central processor(CPU=central processing unit), an application-specific integratedcircuit (ASIC), or any other integrated circuit, respectively.

Computer programs, software programs or programs may be employed, forexample, in the context of the manufacturing process, i.e., for example,for controlling the manufacture of respective embodiments ofmagnetic-field sensors. Respective programs may thus be employed andused in the context of manufacturing plants for controlling same, butalso in the context of designing and in the context of laying outrespective embodiments of magnetic-field sensors. As the above listinghas already shown, processors are not to be understood in the sense ofclassical computer processors only, but also in the sense ofapplication-specific processors as occur, for example, in the context ofmachine tools and other production-relevant installations.

While this invention has been described in terms of several embodiments,there are alterations, permutations, and equivalents which fall withinthe scope of this invention. It should also be noted that there are manyalternative ways of implementing the methods and compositions of thepresent invention. It is therefore intended that the following appendedclaims be interpreted as including all such alterations, permutationsand equivalents as fall within the true spirit and scope of the presentinvention.

What is claimed is:
 1. A magnetic-field sensor comprising: amagnetic-field sensor arrangement; and a back-bias magnet, wherein astructure of the back-bias magnet comprises an inhomogeneousmagnetization.
 2. The magnetic-field sensor as claimed in claim 1,wherein the back-bias magnet is moldable as unitary member and ofcuboidal shape, circular shape, elliptical, or frustum shape.
 3. Themagnetic-field sensor as claimed in claim 2, wherein the back-biasmagnet comprises materials selected from the group consisting offerrites, aluminum-nickel-cobalt (AlNiCo), samarium-cobalt (SmCo) andneodymium-iron-boron (NdFeB).
 4. The magnetic-field sensor as claimed inclaim 1, wherein the inhomogeneous magnetization of the back-bias magnetis symmetrical to a first symmetry line within at least onecross-section of the back-bias magnet.
 5. The magnetic-field sensor asclaimed in claim 4, wherein the first symmetry line is a symmetry lineof a substantially mirror-symmetrical inhomogeneous magnetization withinthe at least one cross-section of the back-bias magnet.
 6. Themagnetic-field sensor as claimed in claim 4, wherein the first symmetryline within the at least one cross-section of the back-bias magnet is asymmetry line of higher order, rotational symmetry, or ellipsoidalsymmetry.
 7. The magnetic-field sensor as claimed in claim 4, whereinthe inhomogeneous magnetization is further symmetrical to the firstsymmetry line within a further cross-section of the back-bias magnet,the further cross-section intersecting the cross-section at the firstsymmetry line.
 8. The magnetic-field sensor as claimed in claim 1,wherein the inhomogeneous magnetization of the back-bias magnet causes amagnetic flux density outside the back-bias magnet.
 9. Themagnetic-field sensor as claimed in claim 3, wherein magnetic fluxcaused by the inhomogeneous magnetization is substantially not confinedto an inside of the back-bias magnet.
 10. The magnetic-field sensor asclaimed in claim 1, wherein the back-bias magnet comprises theinhomogeneous magnetization in at least 50% of a volume of the back-biasmagnet.
 11. The magnetic-field sensor as claimed in claim 4, wherein theat least one cross-section is spanned by a first direction and a seconddirection, the first and second direction not being parallel, andwherein when walking along the second direction for a given coordinatevalue for the first direction, an angle between the second direction anda local direction of magnetization varies at least over a portion of awalking path, the walking path being different from the first symmetryline.
 12. The magnetic-field sensor as claimed in claim 11, wherein theangle varies monotonically when walking along the walking path.
 13. Themagnetic-field sensor as claimed in claim 11, wherein the angle variesnon-monotonically when walking along the walking path, if the walkingpath runs perpendicular to the first symmetry line.
 14. Themagnetic-field sensor as claimed in claim 1, wherein the magnetic-fieldsensor arrangement comprises a first magnetic-field sensor element and asecond magnetic-field sensor element, the first magnetic-field sensorelement being arranged, with respect to the back-bias magnet, such thatthe first magnetic-field sensor element is exposed, with regard to apredetermined spatial direction, to a magnetic flux density caused bythe back-bias magnet and being within a first flux density range, andthe second magnetic-field sensor element being arranged, with respect tothe back-bias magnet, such that the second magnetic-field sensor elementis exposed, with regard to the predetermined spatial direction, to amagnetic flux density caused by the back-bias magnet and being within asecond flux density range.
 15. The magnetic-field sensor as claimed inclaim 14, wherein the first flux density range and the second fluxdensity range enable operation of the first and second magnetic-fieldsensor elements.
 16. The magnetic-field sensor as claimed in claim 14,wherein the first and second flux density ranges only comprise valuessmaller than or equal to 20 mT in magnitude.
 17. The magnetic-fieldsensor as claimed in claim 14, wherein the first flux density rangecomprises flux densities of opposite sign to the second flux densityrange.
 18. The magnetic-field sensor as claimed in claim 15, wherein thefirst and second magnetic-field sensor elements are magneto-resistivesensor elements.
 19. The magnetic-field sensor as claimed in claim 15,wherein the first and second magnetic-field sensor elements are arrangedon a substrate, and wherein the predetermined spatial direction issubstantially parallel to a main surface of the substrate.
 20. Themagnetic-field sensor as claimed in claim 1, wherein the back-biasmagnet is annular or comprises an annular section.